An infinity scarf is such a great wardrobe accessory for your doll. Every doll clothes collection needs several. You can make them in woven fabric or in knit fabric.
The woven fabric scarves can double as hair ribbons if you use soft fabric and the knit scarves can be used as head bands. For a successful head band you really need to use the overlocker on the seams. A zig zag stitch will work but it is difficult to position the head band.
Have a look through this photo tutorial then download the printable instructions. I have also included a pattern piece so if you haven't yet got a quilter's ruler and rotary cutter it is simple to cut out the right size strip.
Cut a strip 3 1/2" wide and 22 1/2" long.
Fold it in half lengthwise.
Stitch the seam starting and finishing 2" from the ends.